51. (a) The centripetal force is given by Eq. 6-18: F =
mv 2 (1)(465)2 = 0.034 N . = R 6.4 × 106
(b) Calling downward (towards the center of Earth) the positive direction, Newton’s second law leads to mg − T = ma where mg = 9.80 N and ma = 0.034 N, calculated in part (a). Thus, the tension in the cord by which the body hangs from the balance is T = 9.80 − 0.03 = 9.77 N. Thus, this is the reading for a standard kilogram mass, of the scale at the equator of the spinning Earth.